Simplifying Complex Fraction

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EdSewersPark
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Simplifying Complex Fraction

Postby EdSewersPark » Tue May 24, 2011 11:05 pm

Question:

I'm guessing I have to get rid of the fractions by multiplying by the LCD, but I feel like I am missing a step in even getting that.

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stapel_eliz
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Postby stapel_eliz » Wed May 25, 2011 12:53 am

EdSewersPark wrote:Question:

I'm guessing I have to get rid of the fractions by multiplying by the LCD...

Yes, that would be the first step. You may want to factor the lower fraction's denominator first, though, so you're clearly aware of what the LCM actually is. :wink:

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MrAlgebra
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Re: Simplifying Complex Fraction

Postby MrAlgebra » Wed May 25, 2011 12:17 pm

EdSewersPark wrote:Question:

I'm guessing I have to get rid of the fractions by multiplying by the LCD, but I feel like I am missing a step in even getting that.

I would be inclined to start like this. Keeping in mind that



We have





Then find the LCD for and go from there.

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Re: Simplifying Complex Fraction

Postby EdSewersPark » Wed May 25, 2011 5:02 pm

and which equals which equals

Then I have

This is where I draw a blank, do I need to change so that it appears in the denominator? Or do I need to find the LCD for and ?

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stapel_eliz
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Postby stapel_eliz » Wed May 25, 2011 9:41 pm

EdSewersPark wrote:

You have two denominators: x - 1 and 1 - x2 = (1 - x)(1 + x). With a "minus" sign, the first denominator becomes -(1 - x). Take the "minus" sign through the numerator, and you get a subtraction on top.

Use the method illustrated here and multiply, top and bottom, by (1 - x2). This will immediately simplify the fraction considerably! :wink:

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Re: Simplifying Complex Fraction

Postby EdSewersPark » Thu May 26, 2011 10:27 pm



Can I cancel out both (x-1)'s and (3x-1)'s at this point?

Would 2(1-x) be the wrong answer?

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stapel_eliz
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Postby stapel_eliz » Thu May 26, 2011 11:31 pm

EdSewersPark wrote:

Can I cancel out both (x-1)'s and (3x-1)'s at this point?

Would 2(1-x) be the wrong answer?

Since 1 - x and x - 1 are not the same, no, they cannot be "cancelled". Instead, try making the change explained earlier. Then see about cancelling. :wink:

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MrAlgebra
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Re: Simplifying Complex Fraction

Postby MrAlgebra » Wed Jun 01, 2011 11:41 pm

EdSewersPark wrote:

Can I cancel out both (x-1)'s and (3x-1)'s at this point?

Would 2(1-x) be the wrong answer?

You're right. It should go:



Canceled out 3x - 1.

Canceled out x - 1.

All that's left.

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Re: Simplifying Complex Fraction

Postby Donut2CoffeeCup » Thu Jun 30, 2011 2:08 pm

Tidy up the top, ie: make it a single fraction:



Now use to get



Factorise

And note (very carefully) that

If you can't see this - reverse the step to check:

So far we have:



To set up the `cancelling' of the term write , so that



Cancel the terms:



Cancel the terms so that you get:



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